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Rapid separation of linear crystals of trapped ions into different subsets is critical for realizing trapped ion quantum computing architectures where ions are rearranged in trap arrays to achieve all-to-all connectivity between qubits. We introduce a general theoretical framework that can be used to describe the separation of same-species and mixed-species crystals into smaller subsets. The framework relies on an efficient description of the evolution of Gaussian motional states under quadratic Hamiltonians that only requires a special solution of the classical equations of motion of the ions to describe their quantum evolution under the influence of a time-dependent applied potential and the ions' mutual Coulomb repulsion. We provide time-dependent applied potentials suitable for separation of a mixed species three-ion crystal on timescales similar to that of free expansion driven by Coulomb repulsion, with all modes along the crystal axis starting and ending close to their ground states. Three separately-confined mixed species ions can be combined into a crystal held in a single well without energy gain by time-reversal of this separation process.

Excess "micromotion" of trapped ions due to the residual radio frequency (rf) trapping field at their location is often undesirable and is usually carefully minimized. Here, we induce precise amounts of excess micromotion on individual ions by adjusting the local static electric field they experience. Micromotion modulates the coupling of an ion to laser fields, ideally tuning it from its maximum value to zero as the ion is moved away from the trap's rf null. We use tunable micromotion to vary the Rabi frequency of stimulated Raman transitions over two orders of magnitude, and to individually control the rates of resonant fluorescence from three ions under global laser illumination without any changes to the driving light fields. The technique is amenable to situations where addressing individual ions with focused laser beams is challenging, such as tightly packed linear ion strings or two-dimensional ion arrays illuminated from the side.

Understanding molecular state evolution is central to many disciplines, including molecular dynamics, precision measurement, and molecule-based quantum technology. Details of the evolution are obscured when observing a statistical ensemble of molecules. Here, we reported real-time observations of thermal radiation-driven transitions between individual states ("jumps") of a single molecule. We reversed these "jumps" through microwave-driven transitions, resulting in a twentyfold improvement in the time the molecule dwells in a chosen state. The measured transition rates showed anisotropy in the thermal environment, pointing to the possibility of using single molecules as in-situ probes for the strengths of ambient fields. Our approaches for state detection and manipulation could apply to a wide range of species, facilitating their uses in fields including quantum science, molecular physics, and ion-neutral chemistry., Comment: 37 pages, 8 figures

Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. RB involves applying known random sequences of gates to an initial state and using the statistics of a final measurement step to determine an effective depolarizing error per step of the sequence, which is a metric of gate quality. Here we investigate the advantages of fully randomized benchmarking, where a new random sequence is drawn for each experimental trial. The advantages of full randomization include smaller confidence intervals on the inferred step error, the ability to use maximum likelihood analysis without heuristics, straightforward optimization of the sequence lengths, and the ability to model and measure behaviors that go beyond the typical assumption of time-independent error rates. We discuss models of time-dependent or non-Markovian errors that generalize the basic RB model of a single exponential decay of the success probability. For any of these models, we implement a concrete protocol to minimize the uncertainty of the estimated parameters given a fixed time constraint on the complete experiment, and we implement a maximum likelihood analysis. We consider several previously published experiments and determine the potential for improvements with optimized full randomization. We experimentally observe such improvements in Clifford randomized benchmarking experiments on a single trapped ion qubit at the National Institute of Standards and Technology (NIST). For an experiment with uniform lengths and intentionally repeated sequences the step error was $2.42^{+0.30}_{-0.22}\times 10^{-5}$, and for an optimized fully randomized experiment of the same total duration the step error was $2.57^{+0.07}_{-0.06}\times 10^{-5}$. We find a substantial decrease in the uncertainty of the step error as a result of optimized fully randomized benchmarking.

Cooling the motion of trapped ions to near the quantum ground state is crucial for many applications in quantum information processing and quantum metrology. However, certain motional modes of trapped-ion crystals can be difficult to cool due to weak or zero interaction between the modes and the cooling radiation, typically laser beams. We overcome this challenge by coupling a mode with weak cooling radiation interaction to one with strong cooling radiation interaction using parametric modulation of the trapping potential, thereby enabling indirect cooling of the former. In this way, we demonstrate near-ground-state cooling of motional modes with weak or zero cooling radiation interaction in multi-ion crystals of the same and mixed ion species, specifically $^9$Be$^+$-$^9$Be$^+$, $^9$Be$^+$-$^{25}$Mg$^+$, and $^9$Be$^+$-$^{25}$Mg$^+$-$^9$Be$^+$ crystals. This approach can be generally applied to any Coulomb crystal where certain motional modes cannot be directly cooled efficiently, including crystals containing molecular ions, highly-charged ions, charged fundamental particles, or charged macroscopic objects., Comment: 16 pages, 8 figures

State readout of trapped-ion qubits with trap-integrated detectors can address important challenges for scalable quantum computing, but the strong rf electric fields used for trapping can impact detector performance. Here, we report on NbTiN superconducting nanowire single-photon detectors (SNSPDs) employing grounded aluminum mirrors as electrical shielding that are integrated into linear surface-electrode rf ion traps. The shielded SNSPDs can be successfully operated at applied rf trapping potentials of up to $\mathrm{54\,V_{peak}}$ at $\mathrm{70\,MHz}$ and temperatures of up to $\mathrm{6\,K}$, with a maximum system detection efficiency of $\mathrm{68\,\%}$. This performance should be sufficient to enable parallel high-fidelity state readout of a wide range of trapped ion species in typical cryogenic apparatus., Comment: 6 pages, 4 figures. The following article has been submitted to Applied Physics Letters

We use quantum-logic spectroscopy (QLS) and interrogate rotational transitions of a single CaH+ ion with a highly coherent frequency comb, achieving a fractional statistical uncertainty for a transition line center of 4 x 10^-13. We also improve the resolution in measurement of the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, which we characterize and model. This allows us to determine the electric dipole moment of CaH+ by systematically displacing the ion to sample different known rf electric fields and measuring the resultant shifts in transition frequency., Comment: 5 pages, 3 figures, plus supplemental material

Precise quantum control and measurement of several harmonic oscillators, such as the modes of the electromagnetic field in a cavity or of mechanical motion, are key for their use as quantum platforms. The motional modes of trapped ions can be individually controlled and have good coherence properties. However, achieving high-fidelity two-mode operations and nondestructive measurements of the motional state has been challenging. Here we demonstrate the coherent exchange of single motional quanta between spectrally separated harmonic motional modes of a trapped-ion crystal. The timing, strength, and phase of the coupling are controlled through an oscillating electric potential with suitable spatial variation. Coupling rates that are much larger than decoherence rates enable demonstrations of high fidelity quantum state transfer and beamsplitter operations, entanglement of motional modes, and Hong-Ou-Mandel-type interference. Additionally, we use the motional coupling to enable repeated non-destructive projective measurement of a trapped-ion motional state. Our work enhances the suitability of trapped-ion motion for continuous-variable quantum computing and error correction and may provide opportunities to improve the performance of motional cooling and motion-mediated entangling interactions., Comment: 27 pages, 12 figures

We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a $^9\text{Be}^+$ qubit ion is mapped to a $^{25}\text{Mg}^+$ readout ion using laser-driven Raman transitions. By partitioning the $^9\text{Be}^+$ ground state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. We demonstrate combined readout and back-action errors for the two subspaces of $1.2^{+1.1}_{-0.6} \times 10^{-4}$ and $0^{+1.9}_{-0} \times 10^{-5}$ with 68% confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection., Comment: 7 + 6 pages, 3 + 1 figures

We investigate the feasibility of using electrons in a linear Paul trap as qubits in a future quantum computer. We discuss the necessary experimental steps to realize such a device through a concrete design proposal, including trapping, cooling, electronic detection, spin readout and single and multi-qubit gate operations. Numeric simulations indicate that two-qubit Bell-state fidelities of order 99.99% can be achieved assuming reasonable experimental parameters.

We demonstrate a simplified method for dissipative generation of an entangled state of two trapped-ion qubits. Our implementation produces its target state faster and with higher fidelity than previous demonstrations of dissipative entanglement generation and eliminates the need for auxiliary ions. The entangled singlet state is generated in $\sim$7 ms with a fidelity of 0.949(4). The dominant source of infidelity is photon scattering. We discuss this error source and strategies for its mitigation., Comment: 12 pages, 6 figures

We present protocols for dissipative entanglement of three trapped-ion qubits and discuss a scheme that uses sympathetic cooling as the dissipation mechanism. This scheme relies on tailored destructive interference to generate any one of six entangled W states in a three-ion qubit space. Using a beryllium-magnesium ion crystal as an example system, we theoretically investigate the protocol's performance and the effects of likely error sources, including thermal secular motion of the ion crystal, calibration imperfections, and spontaneous photon scattering. We estimate that a fidelity of $\sim$ 98 % may be achieved in typical trapped ion experiments with $\sim$ 1 ms interaction time. These protocols avoid timescale hierarchies for faster preparation of entangled states., Comment: Includes additional references

We demonstrate the use of a single trapped ion as a sensor to probe electric-field noise from interchangeable test surfaces. As proof of principle, we measure the magnitude and distance dependence of electric-field noise from two ion-trap-like samples with patterned Au electrodes. This trapped-ion sensor could be combined with other surface characterization tools to help elucidate the mechanisms that give rise to electric-field noise from ion-trap surfaces. Such noise presents a significant hurdle for performing large-scale trapped-ion quantum computations., Comment: 11 pages, 4 figures

Characterization and suppression of noise are essential for the control of harmonic oscillators in the quantum regime. We measure the noise spectrum of a quantum harmonic oscillator from low frequency to near the oscillator resonance by sensing its response to amplitude modulated periodic drives with a qubit. Using the motion of a trapped ion, we experimentally demonstrate two different implementations with combined sensitivity to noise from 500 Hz to 600 kHz. We apply our method to measure the intrinsic noise spectrum of an ion trap potential in a previously unaccessed frequency range., Comment: 6 + 10 pages, 4 + 7 figures

Conventional information processors freely convert information between different physical carriers to process, store, or transmit information. It seems plausible that quantum information will also be held by different physical carriers in applications such as tests of fundamental physics, quantum-enhanced sensors, and quantum information processing. Quantum-controlled molecules in particular could transduce quantum information across a wide range of quantum-bit (qubit) frequencies, from a few kHz for transitions within the same rotational manifold, a few GHz for hyperfine transitions, up to a few THz for rotational transitions, to hundreds of THz for fundamental and overtone vibrational and electronic transitions, possibly all within the same molecule. Here, we report the first demonstration of entanglement between states of the rotation of a $\rm^{40}CaH^+$ molecular ion and internal states of a $\rm^{40}Ca^+$ atomic ion. The qubit addressed in the molecule has a frequency of either 13.4 kHz or 855 GHz, highlighting the versatility of molecular qubits. This work demonstrates how molecules can transduce quantum information between qubits with different frequencies to enable hybrid quantum systems. We anticipate that quantum control and measurement of molecules as demonstrated here will create opportunities for quantum information science, quantum sensors, fundamental and applied physics, and controlled quantum chemistry., Comment: 19 pages, 3 figures

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use generally applicable quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state non-destructively, leaving the molecule ready for further manipulation. We resolve rotational transitions to 11 significant digits and derive the rotational constant of CaH+ to be B_R = 142501777.9(1.7) kHz. Our approach suits a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics., Comment: 25 pages, 4 figures, 6 tables

Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval [0.845, 0.872] at the 95% confidence level. The implementation combines ion shuttling with individually-addressed single-qubit rotations and detections, same- and mixedspecies two-qubit gates, and real-time conditional operations, thereby demonstrating essential tools for scaling trapped-ion quantum computers combined in a single device.

Coherently displaced harmonic oscillator number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a projective measurement via state-dependent fluorescence, with near-unit fidelity. This leads to a rich set of line shapes when recording the internal-state excitation probability after a sideband excitation, as a function of the frequency detuning of the displacement drive with respect to the ion's motional frequency. We precisely characterize the coherent displacement based on the resulting line shapes, which exhibit sharp features that are useful for oscillator frequency determination from the single quantum regime up to very large coherent states with average occupation numbers of several hundred. We also introduce a technique based on multiple coherent displacements and free precession for characterizing noise on the trapping potential in the frequency range of 500 Hz to 400 kHz. Signals from the ion are directly used to find and eliminate sources of technical noise in this typically unaccessed part of the spectrum.

The use of special quantum states to achieve sensitivities below the limits established by classically behaving states has enjoyed immense success since its inception. In bosonic interferometers, squeezed states, number states and cat states have been implemented on various platforms and have demonstrated improved measurement precision over interferometers based on coherent states. Another metrologically useful state is an equal superposition of two eigenstates with maximally different energies; this state ideally reaches the full interferometric sensitivity allowed by quantum mechanics. By leveraging improvements to our apparatus made primarily to reach higher operation fidelities in quantum information processing, we extend a technique to create number states up to $n=100$ and to generate superpositions of a harmonic oscillator ground state and a number state of the form $\textstyle{\frac{1}{\sqrt{2}}}(\lvert 0\rangle+\lvert n\rangle)$ with $n$ up to 18 in the motion of a single trapped ion. While experimental imperfections prevent us from reaching the ideal Heisenberg limit, we observe enhanced sensitivity to changes in the oscillator frequency that initially increases linearly with $n$, with maximal value at $n=12$ where we observe 3.2(2) dB higher sensitivity compared to an ideal measurement on a coherent state with the same average occupation number. The quantum advantage from using number-state superpositions can be leveraged towards precision measurements on any harmonic oscillator system; here it enables us to track the average fractional frequency of oscillation of a single trapped ion to approximately 2.6 $\times$ 10$^{-6}$ in 5 s. Such measurements should provide improved characterization of imperfections and noise on trapping potentials, which can lead to motional decoherence, a leading source of error in quantum information processing with trapped ions.

Entanglement generation can be robust against noise in approaches that deliberately incorporate dissipation into the system dynamics. The presence of additional dissipation channels may, however, limit fidelity and speed of the process. Here we show how quantum optimal control techniques can be used to both speed up the entanglement generation and increase the fidelity in a realistic setup, whilst respecting typical experimental limitations. For the example of entangling two trapped ion qubits [Lin et al., Nature 504, 415 (2013)], we find an improved fidelity by simply optimizing the polarization of the laser beams utilized in the experiment. More significantly, an alternate combination of transitions between internal states of the ions, when combined with optimized polarization, enables faster entanglement and decreases the error by an order of magnitude., Comment: 16 pages, 8 figures

Laser cooling and trapping of atoms and atomic ions has led to numerous advances including the observation of exotic phases of matter, development of exquisite sensors and state-of-the-art atomic clocks. The same level of control in molecules could also lead to profound developments such as controlled chemical reactions and sensitive probes of fundamental theories, but the vibrational and rotational degrees of freedom in molecules pose a formidable challenge for controlling their quantum mechanical states. Here, we use quantum-logic spectroscopy (QLS) for preparation and nondestructive detection of quantum mechanical states in molecular ions. We develop a general technique to enable optical pumping and preparation of the molecule into a pure initial state. This allows for the observation of high-resolution spectra in a single ion (here CaH+) and coherent phenomena such as Rabi flopping and Ramsey fringes. The protocol requires a single, far-off resonant laser, which is not specific to the molecule, so that many other molecular ions, including polyatomic species, could be treated with the same methods in the same apparatus by changing the molecular source. Combined with long interrogation times afforded by ion traps, a broad range of molecular ions could be studied with unprecedented control and precision, representing a critical step towards proposed applications, such as precision molecular spectroscopy, stringent tests of fundamental physics, quantum computing, and precision control of molecular dynamics., Comment: 38 pages in preprint format, 9 figures, 3 tables; added references

We study theoretically the possibilities of coupling the quantum mechanical motion of a trapped charged particle (e.g. ion or electron) to quantum degrees of freedom of superconducting devices, nano-mechanical resonators and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e. the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples, using parameters that are experimentally attainable in the foreseeable future. We conclude that those hybrid quantum system considered involving an atomic ion are unfavorable, compared to using an electron, since the coupling rates between the charged particle and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates which significantly exceed decoherence rates. Moreover it might have appealing properties such as fast entangling gates, long coherence and flexible electron interconnectivity topology. Realizing such a system, however, is technologically challenging, since it requires accommodating both trapping technology and superconducting circuitry in a compatible manner. We review some of the challenges involved, such as the required trap parameters, electron sources, electrical circuitry and cooling schemes in order to promote further investigations towards the realization of such a hybrid system.

Experiments in atomic, molecular, and optical (AMO) physics rely on lasers at many different wavelengths and with varying requirements on spectral linewidth, power, and intensity stability. Vertical external-cavity surface-emitting lasers (VECSELs), when combined with nonlinear frequency conversion, can potentially replace many of the laser systems currently in use. Here we present and characterize VECSEL systems that can perform all laser-based tasks for quantum information processing experiments with trapped magnesium ions. For photoionization of neutral magnesium, 570.6$\,$nm light is generated with an intracavity frequency-doubled VECSEL containing a lithium triborate (LBO) crystal for second harmonic generation. External frequency doubling produces 285.3$\,$nm light for resonant interaction with the $^{1}S_{0}\leftrightarrow$ $^{1}P_{1}$ transition of neutral Mg. Using an externally frequency-quadrupled VECSEL, we implement Doppler cooling of $^{25}$Mg$^{+}$ on the 279.6$\,$nm $^{2}S_{1/2}\leftrightarrow$ $^{2}P_{3/2}$ cycling transition, repumping on the 280.4$\,$nm $^{2}S_{1/2}\leftrightarrow$ $^{2}P_{1/2}$ transition, coherent state manipulation, and resolved sideband cooling close to the motional ground state. Our systems serve as prototypes for applications in AMO requiring single-frequency, power-scalable laser sources at multiple wavelengths., Comment: 6 pages, 9 figures

A custom-built and precisely controlled quantum system may offer access to a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analog quantum simulator that makes the relevant observables, interactions, and states of a quantum model accessible could permit experimental insight into complex quantum dynamics that are intractable on conventional computers. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here we characterise two-dimensional arrays of three ions trapped by radio-frequency fields in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 micrometer. In our approach, which is scalable to arbitrary two dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as tuning of crucial couplings between ions within experimental sequences. Our work paves the way towards an analog quantum simulator of two-dimensional systems designed at will., Comment: 10 pages, 5 figures

A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored non-unitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms., Comment: 5 pages, 4 figures

Quantum simulation - the use of one quantum system to simulate a less controllable one - may provide an understanding of the many quantum systems which cannot be modeled using classical computers. Impressive progress on control and manipulation has been achieved for various quantum systems, but one of the remaining challenges is the implementation of scalable devices. In this regard, individual ions trapped in separate tunable potential wells are promising. Here we implement the basic features of this approach and demonstrate deterministic tuning of the Coulomb interaction between two ions, independently controlling their local wells. The scheme is suitable for emulating a range of spin-spin interactions, but to characterize the performance of our setup we select one that entangles the internal states of the two ions with 0.82(1) fidelity. Extension of this building-block to a 2D-network, which ion-trap micro-fabrication processes enable, may provide a new quantum simulator architecture with broad flexibility in designing and scaling the arrangement of ions and their mutual interactions. To perform useful quantum simulations, including those of intriguing condensed-matter phenomena such as the fractional quantum Hall effect, an array of tens of ions might be sufficient., Comment: To appear in Nature

We report large-mode-area solid-core photonic crystal fibers made from fused silica that resist ultraviolet (UV) solarization even at relatively high optical powers. Using a process of hydrogen loading and UV irradiation of the fibers, we demonstrate stable single-mode transmission over hundreds of hours for fiber output powers of 10 mW at 280 nm and 125 mW at 313 nm (limited only by the available laser power). Fiber attenuation ranges from 0.9 dB/m to 0.13 dB/m at these wavelengths, and is unaffected by bending for radii above 50 mm., Comment: 11 pages, 6 figures

We describe a high-resolution spectroscopy method, in which the detection of single excitation events is enhanced by a complete loss of coherence of a superposition of two ground states. Thereby, transitions of a single isolated atom nearly at rest are recorded efficiently with high signal-to-noise ratios. Spectra display symmetric line shapes without stray-light background from spectroscopy probes. We employ this method on a $^{25}$Mg$^+$ ion to measure one, two, and three-photon transition frequencies from the 3S ground state to the 3P, 3D, and 4P excited states, respectively. Our results are relevant for astrophysics and searches for drifts of fundamental constants. Furthermore, the method can be extended to other transitions, isotopes, and species. The currently achieved fractional frequency uncertainty of $5 \times 10^{-9}$ is not limited by the method., Comment: 5 pages, 4 figures

We present a detailed study of quantum simulations of coupled spin systems in surface-electrode ion-trap arrays, and illustrate our findings with a proposed implementation of the hexagonal Kitaev model [A. Kitaev, Annals of Physics 321,2 (2006)]. The effective (pseudo)spin interactions making up such quantum simulators are found to be proportional to the dipole-dipole interaction between the trapped ions, and are mediated by motion which can be driven by state-dependent forces. The precise forms of the trapping potentials and the interactions are derived in the presence of a surface electrode and a cover electrode. These results are the starting point to derive an optimized surface-electrode geometry for trapping ions in the desired honeycomb lattice of Kitaev's model, where we design the dipole-dipole interactions in a way that allows for coupling all three bond types of the model simultaneously, without the need for time discretization. Finally we propose a simple wire structure that can be incorporated in a microfabricated chip to generate localized state-dependent forces which drive the couplings prescribed by this particular model; such a wire structure should be adaptable to many other situations., Comment: 24 pages, 7 figures. v2: simplified the derivation of (28) without changing conclusions; minor edits. v3: minor edits

We present a solid-state laser system that generates 750 mW of continuous-wave single-frequency output at 313 nm. Sum-frequency generation with fiber lasers at 1550 nm and 1051 nm produces up to 2 W at 626 nm. This visible light is then converted to UV by cavity-enhanced second-harmonic generation. The laser output can be tuned over a 495 GHz range, which includes the 9Be+ laser cooling and repumping transitions. This is the first report of a narrow-linewidth laser system with sufficient power to perform fault-tolerant quantum-gate operations with trapped 9Be+ ions by use of stimulated Raman transitions., Comment: 9 pages, 4 figures

We introduce a general method for designing tailored lattices of magnetic microtraps for ultracold atoms, on the basis of patterned permanently magnetized films. A fast numerical algorithm is used to automatically generate patterns which provide optimal atom confinement while respecting desired lattice symmetries and trap parameters. The algorithm can produce finite and infinite lattices of any plane symmetry; we focus specifically on square and triangular lattices which are of interest to future experiments. Typical trap parameters are discussed as well as the impact of realistic imperfections such as finite lithographic resolution and magnetic inhomogeneity. The presented designer lattices open new avenues for quantum simulation and quantum information processing with ultracold atoms on atom chips., Comment: 11 pages, 5 figures

We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also its phonon number, which makes an ion trap implementation of the quantum walk feasible., Comment: 5 pages, 3 figures

Trapped ions offer long internal state (spin) coherence times and strong inter-particle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices., Comment: 4 pages, 3 figures

Small, controllable, highly accessible quantum systems can serve as probes at the single quantum level to study multiple physical effects, for example in quantum optics or for electric and magnetic field sensing. The applicability of trapped atomic ions as probes is highly dependent on the measurement situation at hand and thus calls for specialized traps. Previous approaches for ion traps with enhanced optical access included traps consisting of a single ring electrode or two opposing endcap electrodes. Other possibilities are planar trap geometries, which have been investigated for Penning traps and rf-trap arrays. By not having the electrodes lie in a common plane the optical access in the latter cases can be substantially increased. Here, we discuss the fabrication and experimental characterization of a novel radio-frequency (rf) ion trap geometry. It has a relatively simple structure and provides largely unrestricted optical and physical access to the ion, of up to 96% of the total 4pi solid angle in one of the three traps tested. We also discuss potential applications in quantum optics and field sensing. As a force sensor, we estimate sensitivity to forces smaller than 1 yN Hz^(-1/2)., Comment: 6 pages, 3 figures. Corrections of some typos, application section expanded to account for reviewer comments